Answered
What action or inaction by the League of Nations caused its critics to conclude that the supranational organization had become irrelevant?
Why the UN is considered irrelevant .
Assuming you mean the UN, it has largely been that the UN is a democratic organization. And because Democracy and Bureaucracy pretty m…uch go together, there is some bureaucratic process in the UN. Democratic organizations also tend to debate quite a lot. This can mean that the UN will debate on something for months on end before making a decision. By then, often something happens that either makes the decision irrelevant, or reverses the decision, causing another three months of debate. While the UN is indeed the most powerful organization other than the US for international politics, it is incredibly inefficient and very hesitant to take action that actually has serious consequences for a country. .
Another problem is that its security council has several 'set' members that cannot be changed. Some, arguably, no longer have enough international influence to hold such a position, while other countries that perhaps should be permanent members of this council are not members. Also, the fact that any country on the council can prevent any action of the council with a single veto vote means that all must agree for anything to actually occur. Only rarely does this happen, especially since the United States and Russia often have very different international interests. Case in point, Russia has used its veto several times to protect Iran from reprisals and certain types of sanctions. .
ANSWER .
No, it is not the UN!!! The League of Nations was a Treaty somewhat similar to the UN but it was created after the end of WW I initially by the Americans, French and British. Its main flaw is that it had no organization and no rules that would effectively punish a member state from initiating an aggressive conflict on another state. The historic moments that deemed the League of Nations irrelevant were the invasion of China by Japan started in 1932 with the creation of the puppet-state Manchukuo by Japan in the North-East of China (the LoN protested but did nothing against Japan) and the invasion of Ethiopia by Italy in 1935 which produced no notable reaction from the League of Nations..
There was also at issue the fact that several of the more powerful countries were not members - including the United States. Despite the efforts taken by its president at the time, congress refused to ratify the treaty that would have made the United States a member. Not only the United States, but several other major countries as well were not members, severely limiting the effectiveness and power of the League of Nations. (MORE)